Many wireless applications utilize saturated radio RF amplifiers because of their high efficiency. Constant envelope modulations are used with saturated amplifiers because the transmitted information resides in the phase domain, which is relatively unaffected by the nonlinearity of the saturated amplifier. Minimum Shift Keying (MSK), Gaussian MSK (GMSK), and other forms of continuous phase modulation (CPM) can be applied to navigational signals to obtain reduced bandwidth while maintaining a constant envelope. For example, in MSK, a linear ramp phase transition is used instead of an instantaneous phase transition.
Two conventional phase shift keying cases to consider are: binary antipodal schemes, e.g., Binary Phase Shift Keying (BPSK); and M-ary PSK. With BPSK, if a single pseudo-noise (PN) code is to be transmitted on a single quadrature channel, then a binary form of MSK can be used to transmit the code. In this case, two phases that are 180° apart (i.e., “antipodal” phase states) can be used to respectively represent the binary signal states. When using continuous phase transitions between symbols instead of instantaneous phase transitions, there are two equivalent phase trajectory option available to perform the 180° phase transition between the two antipodal phases: proceed in the counterclockwise direction for a total phase change of 180° (a positive phase shift ramp); or proceed in the clockwise direction for a total phase change of −180° (a negative phase shift ramp).
These two options are illustrated in FIG. 1 for the case where the current symbol is a logical ‘1’ at a phase of 0° and the next symbol is a logical ‘0’ at a phase of 180°. Note that an instantaneous phase change would proceed directly back and forth along the I-axis in the example shown in FIG. 1 (i.e., there is no rotational polarity); thus, the issue of phase rotation polarity exists in the context of phase modulated signals that employ continuous phase transitions between adjacent symbols. Either rotational polarity will result in the same end phases and both are identical in terms of the PN code and the CPM. Thus, the continuous phase modulation leaves an ambiguity with respect to the polarity of the phase ramps when transitioning between antipodal phase states.
A CPM BPSK phase trajectory with a fixed, positive phase transition rotational polarity is illustrated in FIG. 2. In this case, the symbol vector proceeds with a counterclockwise phase rotation around the unit circle for all phase transitions, i.e., from a logical ‘1’ at 0° to a logical ‘0’ at 180° and from a logical ‘0’ at 180° to a logical ‘1’ at 0°.
Alternating phase transition rotational polarity per transition is shown in FIG. 3. In this case, the symbol vector rotates back and forth from a logical ‘1’ at 0° to a logical ‘0’ at 180°. That is, a counterclockwise (positive) phase rotation is used to transition from the ‘1’ phase state to the ‘0’ phase state, while a clockwise (negative) phase rotation is used to transition from the ‘0’ phase state to the ‘1’ phase state. Note that in this scheme, the phase trajectory always stays in the upper half plane (as illustrated) or, alternatively, in the lower half plane if the opposite polarity convention is used (not shown). The quadrature (Q) component of the signal will therefore always be either positive (as shown in FIG. 3) or negative (in the convention not shown) for all phase transitions.
The problem with a fixed rotation polarity such as that shown in FIG. 2 is that, if the same direction of rotation is used for all phase transitions, there is a net frequency shift which skews the frequency spectrum of the signal. There is also spreading of the PN symbol information into the next symbol which results in a widening of the autocorrelation peak and a filling in of the side nulls. This degrades the time acquisition performance of the user receiver, which is particularly troublesome for receivers required to accurately determine the arrival time of signals, such as in the case of navigation signals. These effects are shown in FIGS. 4 and 5 for a CPM version of a BOC(10,5) (Binary Offset Carrier) waveform with a fixed phase rotation direction. Specifically, FIG. 4 illustrates the correlation function degradation of a BOC(10,5) CPM signal with a fixed phase rotation direction (solid line) relative to a conventional BOC(10,5) correlation function with instantaneous phase transitions (dashed line). FIG. 5 illustrates the power spectrum of a CPM BOC(10,5) with a fixed phase rotation direction (solid line) relative to the conventional BOC(10,5) power spectrum with instantaneous phase transitions (dashed line). Note that, as expected the CPM achieves a significantly narrower spectrum than the BOC(10,5) waveform with instantaneous phase transitions. However, the fixed phase rotation of the CPM signal results in the overall spectrum being asymmetric, shifted to the right (positive frequency direction).
The problem with alternating rotation with each transition, as shown in FIG. 3, is that, since the Q component has the same polarity for all transitions, the Q component can be looked at as a stream of pulses with a fixed polarity pulse occurring during each phase transition. This generates unwanted clock spurs and also degrades the null depth of the autocorrelation function.
Thus, when conventional CPM methods (including MSK, GMSK, etc.) are used, the waveform may be bandwidth efficient but will have a distorted correlation function when detected in the user receiver. The correlations nulls that occur at integer chip spacings will not be as deep as for a conventional signal, as shown in FIG. 4. As a result of the decreased null depths, time accuracy estimates in the receiver (Early/Late) detector will be degraded. This happens because some of the energy in each navigational chip is spread into the adjacent chip so that the cross-correlation of the waveform with the reference code is no longer zero at +/−half chip offset.
Where there is PN data on both the in-phase (I) and quadrature (Q) channels, such as with quadrature PSK (QPSK) or M-ary phase constellations, CPM can also be used to maintain a constant envelope. However, the possibility of +180° or −180° phase transitions between adjacent symbols still exists. Thus, M-ary PSK schemes still present the issue of ambiguity with respect to antipodal transitions and, consequently, the same problems that occur in the antipodal case. Further, in cases where there are multiple codes such that one code is on the I channel and another code is on the Q channel, or where multiple codes are combined to form an M-ary signal constellation (e.g., Phase-Optimized Constant-Envelope Transmission (POCET), Interplex, Majority Vote, or Intervote combining methods), the same issues described above for the antipodal case will arise when there are 180° phase transitions between adjacent symbols.
Conventional MSK and GMSK are defined to have the phase transition occurring over the entire symbol interval. In the case of GMSK, the waveform is further tailored through varying the BT product where B is the Gaussian filter bandwidth and T is the symbol time. However this approach offers only a limited amount of optimization of bandwidth efficiency versus correlation loss.
In conventional CPM systems, the spectrum is controlled only by the modulation parameters. In the case of GMSK, for example, this would be the BT product. This does not always offer a system designer enough options for designing a waveform that meets desired spectral requirements.